A popular technique for demodulating FM signals in a telecommunications receiver involves employing a discriminator to extract the signal of interest. Typically, once received, a modulated FM signal is converted to base band by extracting the in-phase (I) and quadrature-phase (Q) components where:
I(t)=a(t) cos .phi.(t); PA1 Q(t)=a(t) sin .phi.(t); PA1 .phi.(t)=.intg..omega.(.tau.)d.tau.; and PA1 .omega.(.tau.) is the information bearing signal.
Once the I and Q components are determined, the discriminator operation evaluates the quantity: EQU I(t)Q'(t)-Q(t)I'(t)=.alpha..sup.2 (t).phi.'(t)=.alpha..sup.2 (t).omega.(t)
where ' denotes the derivative. In cases where the envelope a(t) is constant, the discriminator produces an output proportional to the information bearing signal .omega.(t).
In data communications applications, .omega.(t) is typically a multilevel pulse-amplitude modulation (PAM) signal. Many applications for such signals include more than two signal levels to achieve greater information processing capacity. However, in establishing multiple signal levels, the probabilities of decisional errors increase substantially. To combat this problem, a set of thresholds for classifying the signals can be optimally determined to achieve the lowest possible decision error probabilities.
Optimally selecting sets of thresholds theoretically presents an acceptable solution to the problems involved in multi-level demodulation of signals within a relatively constant envelope. Realistically however, the envelope a(t) always changes, together with the output levels of the discriminator. When this occurs, the predetermined thresholds are no longer optimum and performance degradations in terms of error bit rate increase.
To minimize fluctuations in the envelope, conventional analog discriminators employ additional automatic gain control AGC circuitry to maintain a(t) within an acceptable band of values. Unfortunately, conventional analog AGC circuits have been found to reduce performance degradations only to a limited extent. Moreover, typical wireless channels often exhibit frequency fadings where a(t) has sudden and dramatic changes for which the AGC cannot adapt at all.
In the digital domain, an information-bearing signal may be explicitly extracted without any dependency on the envelope by employing a digital signal processor (DSP) to evaluate the relation: ##EQU1##
The relationship above represents a digital discriminator including a special type of AGC that eliminates the adverse effect of the envelope fluctuation. While this relationship works well to solve the problem of gain fluctuation, evaluation of the inverse function embedded therein typically requires an undesirably high number of instruction cycles. For example, implementation of the inverse function 1/x in the instruction language of the DSP16000 processor available from Lucent Technologies, requires 55 cycles. This is mainly attributeable to the multiplicative and additive nature of most DSP's.
DSP architectures are typically designed to maximize processing speed with a finite number of processor instructions. With each instruction taking a certain amount of time to carry out, eliminating unnecessary instructions substantially increases a DSPs' performance. One common performance or efficiency benchmark utilized in the industry takes into account the number of MIPs, or millions of instructions per second, that the DSP is capable of carrying out. The greater the number, the more efficient the architecture is considered.
One approach to evaluate an inverse function utilizing a DSP assumes that the squared components of I and Q remain constant over several samples. Unfortunately, this technique fails to solve the problem associated with the unacceptably high number of cycles required to carry out the inversion operation.
Therefore, the need exists for an FM digital discriminator and method utilizing automatic gain control to extract signals defined by an inverse function from demodulated signals with a minimum number of instruction cycles on the part of the DSP. The discriminator and method of the present invention satisfy these needs.
The discriminator and method of the present invention allow digital signal processors to extract signals characterized by an inverse function from FM demodulated waveforms with a minimum number of instruction cycles. By minimizing instruction cycles, the DSP's limited instruction resources may be conserved to carry out additional functions and improve processor efficiency.
To realize the advantages above, the invention in one form comprises a method for use with a digital signal processor to extract an information bearing signal .omega.(n) from a base-band signal in the form of an inverse function. The processor includes memory and utilizes a minimum number of instructions stored in the memory. The base-band waveform comprises a plurality of complex-valued samples having respective I and Q components. The method includes the steps of receiving a first sample at an instant n having respective I(n) and Q(n) components and defining an interval for evaluating potential values for the I(n) and Q(n) components. Next, said I(n) and Q(n) components are transformed so as to have respective threshold values residing in the predefined interval. Then, a step of estimating the transformed components with a series of non-inverted polynomial functions is carried out over the predefined interval. The method proceeds by extracting the information-bearing signal with the digital signal processor operating according to the instructions to evaluate the series of non-inverted polynomial functions.
In another form, the invention comprises an FM discriminator for use in a digital signal processor to extract an information-bearing signal from a base-band signal. The base-band signal is in the form of an inverse function and comprises a plurality of complex-valued samples having respective I and Q components. The discriminator includes an input for receiving a first sample at an instant n having respective I(n) and Q(n) components, a memory, and logic disposed in communication with said input and the memory. The logic defines an interval for evaluating potential values for said I(n) and Q(n) components, then transforms the I(n) and Q(n) components to have respective threshold values residing in the predefined interval. The logic also estimates the transformed components with a series of non-inverted polynomial functions over the predefined interval, and extracts the information-bearing signal by means of the digital signal processor, to evaluate the series of non-inverted polynomial functions. The logic then stores the extracted signal in the memory.